Median for metric spaces

Nacereddine Belili, and Henri Heinich. "Median for metric spaces." Applicationes Mathematicae 28.2 (2001): 191-209. <http://eudml.org/doc/279825>.

@article{NacereddineBelili2001,
abstract = {We consider a Köthe space $(,||·||_)$ of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that $||d(X,Y)||_ ≤ ||d(X,Z)||_$ for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications.},
author = {Nacereddine Belili, Henri Heinich},
journal = {Applicationes Mathematicae},
keywords = {median; metric spaces; conditional median; convergence of medians; Doss expectations; Köthe spaces},
language = {eng},
number = {2},
pages = {191-209},
title = {Median for metric spaces},
url = {http://eudml.org/doc/279825},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Nacereddine Belili
AU - Henri Heinich
TI - Median for metric spaces
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 2
SP - 191
EP - 209
AB - We consider a Köthe space $(,||·||_)$ of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that $||d(X,Y)||_ ≤ ||d(X,Z)||_$ for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications.
LA - eng
KW - median; metric spaces; conditional median; convergence of medians; Doss expectations; Köthe spaces
UR - http://eudml.org/doc/279825
ER -